The Apple Thunderbolt Display has a cable with both a Thunderbolt connector for audio/video/ethernet, and a MagSafe connector so that the display could power a laptop and effectively operate as a docking station.

It seems that this adapter could handle the audio/video and perhaps the ethernet as well, but I assume that the laptop would need to use a second USB-C for power.

Currently, if I connect my Apple Thunderbolt Display to my old MacbBook Pro via Thunderbolt 2. I can access devices such as USB thumb-drives, external hard drives, other thunderbolt devices and even ethernet connection.

My Question:

If I connect the Apple Thunderbolt Display to the new MacBook Pro's Thunderbolt 3 via this adapter (Thunderbolt 3 to Thunderbolt 2). Will I be able to access, file transfer and make use of these ports on the back of the display through the new MacBook Pro late 2016?
If not all of the ports, which ones?

Just purchased a USB-C ext. drive that I want to use for my Time Machine B/U with an older MBP 15 that uses TB2. The new drive will connect to my USB-2 port but I want the faster TB2 speed. What adapter can I buy that will connect the USB-C to the TB2 port on my mac?